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Understanding Rates and Unit Rates: Making Sense of Quantitative Comparisons

This guide explains rates and unit rates, which compare two quantities with different units of measure. Examples include rates like $23 per foot and 55 mph, while unit rates simplify these comparisons to a denominator of 1 for easy understanding. The document provides practical scenarios, such as calculating average fuel consumption in miles per gallon and average speed in miles per hour. It also covers estimating unit rates for quick calculations and understanding unit prices for cost-effective purchases. Learn the concepts clearly and enhance your mathematical skills!

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Understanding Rates and Unit Rates: Making Sense of Quantitative Comparisons

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  1. 5.2 Rates and Unit Rates

  2. Rate (of a per b): Ratio that compares two quantities with different units of measure. • EX: $23 per foot • EX: 55 mph • EX: $5/person Ratio: 90 3 90 miles 3 hours “90 miles per 3 hours.” Rate:

  3. Unit Rate: • A rate with a denominator of 1 Example: Your family drove 400 miles in 8 hours. The total amount of fuel used was 20 gallons of gas. • What was the average rate of fuel consumption (miles per gallon)? • 2) What was the average rate of speed (miles per hour)? = miles per gallon = mph

  4. 320 feet 8 seconds 313 feet 8 seconds 450 students 90 computers 450 students 91 computers   5 students 1 computer 40 feet 1 second   Estimating Unit Rates: Round one of the #’s so you can divide easily  450 students to 91 computers 313 feet in 8 seconds

  5. Unit Price: Same as unit rate; used to compare price per item - found by $ divided by # of items ($/item). Example: A 16 oz box of cereal costs $2.89 and a 20 oz box costs $3.49. Which is the better buy? = $0.18 per oz. So, the 20 oz. is a better deal!  (cheaper)! = $0.17 per oz.

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